A Brief History of Jazz
Listening to other jazz musicians is by far the most important single thing you can do to learn about jazz improvisation. Just as no words can ever describe what a Monet painting looks like, no primer I can write will describe what Charlie Parker sounds like. While it is important for a performer to develop his own style, this should not be done in isolation. You should be aware of what others have done before you.
Having established the importance of listening, the question remains, "What should I listen to?" Most likely, you already have some idea of jazz musicians you like. Often, you can start with one musician and work outwards. For example, the first jazz musician I listened to extensively was the pianist Oscar Peterson. After buying half a dozen or so of his albums, I found I also liked some of the musicians with whom he had performed, such as trumpet players Freddie Hubbard and Dizzy Gillespie, and started buying their albums as well. Then, upon hearing pianist Herbie Hancock with Hubbard, I found a new direction to explore, one which lead me to trumpet player Miles Davis, and thereby to saxophonist John Coltrane, and the process is still continuing.
Part of the goal of this primer is to help direct you in your listening. What follows is a brief history of jazz, with mention of many important musicians and albums. Note that the subject of jazz history has generated entire volumes. A few of these are listed in the bibliography.
This primer gives a cursory overview of major periods and styles. There is a lot of overlap in the eras and styles described. The later sections on jazz theory are based primarily on principles developed from the 1940's through the 1960's. This music is sometimes referred to as mainstream or straightahead jazz.
Your local library can be an invaluable asset in checking out musicians with whom you are unfamiliar. Also, you may wish to share albums with friends. Taping records or CD's for use by others is, of course, in violation of copyright law, however, and it devalues the musicians' economic reward. You should use the library, and other people's collections, to give you an idea of what you like, and then go out and buy it.
Top Ten List
It is certainly not expected that you run out and purchase albums by all of the artists mentioned above. In general, the artists described first and in the most detail within a given style are considered the most important. A fairly non-controversial "Top Ten List", containing representatives of several styles and instruments, would be Louis Armstrong, Duke Ellington, Billie Holiday, Charlie Parker, Art Blakey, Charles Mingus, Thelonious Monk, Miles Davis, John Coltrane, and Ornette Coleman. These are among the true giants of jazz. After this, personal preferences begin to come more into play.